Fourier analysis (MSAP4-01A)#

import star_privateer as sp
import plato_msap4_demonstrator_datasets.plato_sim_dataset as plato_sim_dataset
import numpy as np
import matplotlib.pyplot as plt
import pandas as pd

K2: Rotation period analysis#

t, s, dt = sp.load_k2_example ()
fig, ax = plt.subplots (1, 1, figsize=(8,4))

ax.scatter (t[s!=0]-t[0], s[s!=0], color='black',
            marker='o', s=1)

ax.set_xlabel ('Time (day)')
ax.set_ylabel ('Flux (ppm)')

fig.tight_layout ()
../../_images/fourier_analysis_5_0.png

As we want to recover rotation periods below 45 days, we only consider the section of the periodogram verifying \(P < P_\mathrm{cutoff} = 60\) days.

pcutoff = 60

As a preprocessing step, we compute the Lomb-Scargle periodogram (in the SAS framework, it will be directyly provided by MSAP1).

p_ps, ls = sp.compute_lomb_scargle (t, s)

Now we perform the periodogram analysis.

cond = p_ps < pcutoff
(prot, e_p, E_p,
 _, param, h_ps) = sp.compute_prot_err_gaussian_fit_chi2_distribution (p_ps[cond], ls[cond], n_profile=20,
                                                                       threshold=0.1, plot_procedure=False,
                                                                       verbose=False)
fig= sp.plot_ls (p_ps, ls, filename='figures/fourier_k2.png', param_profile=param,
                 logscale=False, xlim=(0.1, 5))
../../_images/fourier_analysis_11_0.png
IDP_SAS_PROT_FOURIER = sp.prepare_idp_fourier (param, h_ps, ls.size,
                                              pcutoff=pcutoff, pthresh=None,
                                              pfacutoff=1e-6)

df = pd.DataFrame (data=IDP_SAS_PROT_FOURIER)
df
0 1 2 3 4
0 2.786835 0.027592 0.028150 18241.430962 1.000000e-16
1 1.393417 0.013796 0.014075 9355.805501 1.000000e-16
2 0.786985 0.056182 0.065540 2472.622236 1.000000e-16
df.to_latex (buf='data_products/idp_sas_prot_fourier_k2_211015853.tex',
             formatters=['{:.2f}'.format, '{:.2f}'.format, '{:.2f}'.format,
                         '{:.2f}'.format, '{:.0e}'.format],
             index=False, header=False)
np.savetxt ('data_products/IDP_SAS_PROT_FOURIER_K2.dat',
             IDP_SAS_PROT_FOURIER)

PLATO: Rotation period analysis#

The PLATO simulation below encompasses both rotational modulation and low-frequency modulations due to activity. In order to analyse the rotational signal, we first filter out frequencies above 60 days (in PLATO, this will be done outside MSAP4).

filename = sp.get_target_filename (plato_sim_dataset, '040', filetype='csv')
t, s, dt = sp.load_resource (filename)
s_filtered = sp.preprocess (t, s, cut=60)
fig, ax = plt.subplots (1, 1, figsize=(8,4))

ax.scatter (t[s!=0]-t[0], s[s!=0], color='black',
            marker='o', s=1, label="Unfiltered")
ax.scatter (t[s!=0]-t[0], s_filtered[s_filtered!=0], color='darkorange',
            marker='o', s=1, label="Filtered")

ax.set_xlabel ('Time (day)')
ax.set_ylabel ('Flux (ppm)')

ax.legend ()

fig.tight_layout ()
../../_images/fourier_analysis_17_0.png

As we want to recover rotation periods below 60 days, we only consider the section of the periodogram verifying \(P < P_\mathrm{cutoff} = 60\) days.

pcutoff = 60

As a preprocessing step, we compute the Lomb-Scargle periodogram (in the SAS framework, it will be directyly provided by MSAP1).

p_ps, ls = sp.compute_lomb_scargle (t, s_filtered)

Now we perform the periodogram analysis.

cond = p_ps < pcutoff
(prot, e_p, E_p,
 _, param, h_ps) = sp.compute_prot_err_gaussian_fit_chi2_distribution (p_ps[cond],
                                                                       ls[cond],
                                                                       n_profile=20,
                                                                       threshold=0.1,
                                                                       verbose=False)
sp.plot_ls (p_ps, ls, filename='figures/fourier_plato_short.png', param_profile=param,
            logscale=False, xlim=(1, pcutoff),
            ylim=(1e-3, 1.25e6),
            )
IDP_SAS_PROT_FOURIER = sp.prepare_idp_fourier (param, h_ps, ls.size,
                                                  pcutoff=pcutoff, pthresh=None,
                                                  pfacutoff=1e-6)
df = pd.DataFrame (data=IDP_SAS_PROT_FOURIER)
df
0 1 2 3 4
0 25.969122 2.720310 3.441268 791101.027115 1.000000e-16
1 36.172726 3.871280 4.925569 660816.783569 1.000000e-16
2 50.083306 2.931017 3.319557 99449.921037 1.000000e-16
3 19.091161 2.501881 3.390534 93860.256080 1.000000e-16
../../_images/fourier_analysis_23_1.png
df.to_latex (buf='data_products/idp_sas_prot_fourier_plato_040.tex',
             formatters=['{:.2f}'.format, '{:.2f}'.format, '{:.2f}'.format,
                         '{:.2f}'.format, '{:.0e}'.format],
             index=False, header=False)
np.savetxt ('data_products/IDP_SAS_PROT_FOURIER_PLATO.dat',
             IDP_SAS_PROT_FOURIER)

PLATO: Long term modulation analysis#

This time, we are interested in recovering long term modulations. We consider the section of the periodogram verifying \(P > P_\mathrm{tresh} = 60\) days.

pthresh = 60

As a preprocessing step, we compute the Lomb-Scargle periodogram (in the SAS framework, it will be directyly provided by MSAP1).

p_ps, ls = sp.compute_lomb_scargle (t, s)

Now we perform the periodogram analysis.

(plongterm, e_p, E_p,
 _, param, h_ps) = sp.compute_prot_err_gaussian_fit_chi2_distribution (p_ps[p_ps>pthresh],
                                                                       ls[p_ps>pthresh],
                                                                       n_profile=5,
                                                                       threshold=0.1,
                                                                       verbose=False)
fig = sp.plot_ls (p_ps, ls, filename='figures/fourier_plato_long.png', param_profile=param,
                    logscale=False, xlim=(1,8*pthresh))
IDP_SAS_LONGTERM_MODULATION_FOURIER = sp.prepare_idp_fourier (param, h_ps, ls.size,
                                                                 pcutoff=None, pthresh=pthresh,
                                                                 pfacutoff=1e-6)
df = pd.DataFrame (data=IDP_SAS_LONGTERM_MODULATION_FOURIER)
df
0 1 2 3 4
0 347.077309 16.527491 18.267227 8.754753e+06 1.000000e-16
1 694.154619 33.054982 36.534454 2.280495e+06 1.000000e-16
../../_images/fourier_analysis_31_1.png
df.to_latex (buf='data_products/idp_sas_longterm_modulation_fourier_plato_040.tex',
             formatters=['{:.2f}'.format, '{:.2f}'.format, '{:.2f}'.format,
                         '{:.2f}'.format, '{:.0e}'.format],
             index=False, header=False)
np.savetxt ('data_products/IDP_SAS_LONGTERM_MODULATION_FOURIER_PLATO.dat',
             IDP_SAS_LONGTERM_MODULATION_FOURIER)